The problem is that the InDesign doc is using Minion whereas the Word doc is using Times New Roman. The characters are there in Word, but Minion in InDesign shows the typical box with an X for some of the characters. I hope that clarifies it.
That makes more sense. InDesign is rendering the characters just fine in fonts that have an appropriate set of glyphs, you're just finding out that your chosen font (Minion) doesn't have the necessary combining diacritics. In your shoes, I personally would stop using Minion and shift to a font that actually supports the glyphs I'd need to work in a given language, but you could easily just manually kern stuff into place, or alternately use Peter's script that automates a lot of the manual kerning work.
If you don't already read Yoruba, I'd encourage you to think about switching to a font that supports your language. There are quite a few of them out there; it's just a technology that Adobe fonts don't seem to use, typically. There's no wy to search fonts.adobe.com for fonts that have support for Yoruba, and there's no way (so far as I know) to search for fonts that have combining diacriticals. So in your shoes, I'd personally switch to something generic from Microsoft (many of MS Typography's fonts support combining diacriticals) or perhaps a font like Gentium from SIL, that was made to support such languages, and has a very wide array of combining diacricial marks. But if you're wedded to Myriad, seems to me that we've already established that learning how to use Peter's compositon script is the least bad way for you to proceed.